The Applicant has recently conducted various studies and tests to make bicycle wheel rims using structural fiber based material, typically carbon fiber based material. The advantage offered by this type of material is that of being light in weight with respect to the metallic materials used in the past given equal structural characteristics. Making a rim out of a single part of carbon fiber based material was difficult, at least utilizing the technologies available at that time, due to the typical conformation of the circumferential anchoring wings of the tire. Typically, these wings present peripheral outer edges folded one towards the other thus creating an undercut, which causes the molding problems.